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Verify a(b-c)=ab-ac for a=1.6;b=1/-2;& c=-5/-7​

User Daniel Qiu
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1 Answer

7 votes

Given:


a=1.6,b=(1)/(-2),c=(-5)/(-7)

To verify:


a(b-c)=ab-ac for the given values.

Solution:

We have,


a=1.6,b=(1)/(-2),c=(-5)/(-7)

We need to verify
a(b-c)=ab-ac.

Taking left hand side, we get


a(b-c)=1.6\left((1)/(-2)-(-5)/(-7)\right)


a(b-c)=1.6\left(-(1)/(2)-(5)/(7)\right)

Taking LCM, we get


a(b-c)=1.6\left((-7-10)/(14)\right)


a(b-c)=(16)/(10)\left((-17)/(14)\right)


a(b-c)=(8)/(5)\left((-17)/(14)\right)


a(b-c)=-(68)/(35)\right)

Taking right hand side, we get


ab-ac=1.6* (1)/(-2)-1.6* (-5)/(-7)


ab-ac=-(16)/(20)-(8)/(7)


ab-ac=-(4)/(5)-(8)/(7)

Taking LCM, we get


ab-ac=(-28-40)/(35)


ab-ac=(-68)/(35)

Now,


LHS=RHS

Hence proved.

User Majed
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